(* Basic_2A1: uses: lsx_ind *)
lemma lfsx_ind: ∀h,o,G,T. ∀R:predicate lenv.
(∀L1. G ⊢ ⬈*[h, o, T] 𝐒⦃L1⦄ →
- (â\88\80L2. â¦\83G, L1â¦\84 â\8a¢ â¬\88[h, T] L2 â\86\92 (L1 â\89¡[h, o, T] L2 → ⊥) → R L2) →
+ (â\88\80L2. â¦\83G, L1â¦\84 â\8a¢ â¬\88[h, T] L2 â\86\92 (L1 â\89\9b[h, o, T] L2 → ⊥) → R L2) →
R L1
) →
∀L. G ⊢ ⬈*[h, o, T] 𝐒⦃L⦄ → R L.
(* Basic_2A1: uses: lsx_intro *)
lemma lfsx_intro: ∀h,o,G,L1,T.
- (â\88\80L2. â¦\83G, L1â¦\84 â\8a¢ â¬\88[h, T] L2 â\86\92 (L1 â\89¡[h, o, T] L2 → ⊥) → G ⊢ ⬈*[h, o, T] 𝐒⦃L2⦄) →
+ (â\88\80L2. â¦\83G, L1â¦\84 â\8a¢ â¬\88[h, T] L2 â\86\92 (L1 â\89\9b[h, o, T] L2 → ⊥) → G ⊢ ⬈*[h, o, T] 𝐒⦃L2⦄) →
G ⊢ ⬈*[h, o, T] 𝐒⦃L1⦄.
/5 width=1 by lfdeq_sym, SN_intro/ qed.